60.1.46 problem Problem 60

Internal problem ID [15174]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 60
Date solved : Thursday, October 02, 2025 at 10:06:42 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 20

ode:=(4*y(x)+2*x+3)*diff(y(x),x)-2*y(x)-x-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x}{2}+\frac {\operatorname {LambertW}\left (c_1 \,{\mathrm e}^{5+8 x}\right )}{8}-\frac {5}{8} \]

✓ Mathematica. Time used: 2.329 (sec). Leaf size: 39

ode=(4*y[x]+2*x+3)*D[y[x],x]-2*y[x]-x-1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{8} \left (W\left (-e^{8 x-1+c_1}\right )-4 x-5\right )\\ y(x)&\to \frac {1}{8} (-4 x-5) \end{align*}

✓ Sympy. Time used: 0.697 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (2*x + 4*y(x) + 3)*Derivative(y(x), x) - 2*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x}{2} + \frac {W\left (C_{1} e^{8 x + 5}\right )}{8} - \frac {5}{8} \]